In electronics a NOT gate is more commonly called an inverter. The circle on the symbol is called a bubble, and is used in logic diagrams to indicate a logic negation between the external logic state and the internal logic state (1 to 0 or vice versa).
A weather watch, on the other hand, typically refers to an alert issued to indicate that conditions are favorable for the development of dangerous weather patterns, although the dangerous weather conditions themselves are not currently present.
An example of a tornado watch for parts of Kansas and Nebraska, issued by the Storm Prediction Center on May 5, 2007. A tornado watch (SAME code: TOA) is issued when weather conditions are favorable for the development of severe thunderstorms that are capable of producing tornadoes. A tornado watch therefore implies that it is also a severe thunderstorm watch. A tornado watch must not be confused with a tornado warning. In most cases, the potential exists for large hail and/or damaging winds in addition to tornadoes. A watch does not mean that the severe weather is actually occurring, only that atmospheric conditions have created a significant risk for it.